Lesson7 03-16 and 03-17 Unit 3 Unit 3 Patterns, Computation, and Algebra GLE’S Addressed: #12 Evaluate algebraic expressions containing exponents (especially 2 and 3) and square roots, using substitution (A-1-M) #13 Determine the square root of perfect squares and mentally approximate other square roots by identifying the two whole numbers between which they fall (A-1-M) #39 Analyze and describe simple exponential number patterns (e.g., 3, 9, 27 or 31, 32, 33) (P-1-M) Objective(s) 1. The student will evaluate expressions containing exponents (especially 2 and 3) and square roots, using substitution. 2. The student will determine the square root of perfect squares and mentally approximate other square roots by identifying the two whole numbers between which they fall. 3. The student will analyze and describe simple exponential number patterns. Materials: Daily problem Transparency 7.1 3 boxes of graduated sizes Student Activity 7.1 Transparency 7.2 Student Activity 7.2 Student Activity 7.3/ Homework “What’s My Value?” Student Activity 7.4/iLEAP Connection Index cards for number line in action #7 Text: Estimating Square Roots 11-2 pg. 475-477 RM: 614-618 iLEAP booklet pages 22, 23 Daily Problem Lesson 7 Make the correct substitutions on the left from the given values on the right. 1.
7 a. x
8 2. x² = 9 b. x = 49 3. x³ = 8 c. x = 3 4.
x d. x
2 Answer= 1 – b, 2 – c, 3 –d, 4 - a Have the students come up with their own definition of “square root.” Use the square feet models that were made in lesson 6 to help them see the ‘square root’ relationship to area. Lesson Procedure 1. Discuss Daily Problem. 2. Give each student 4 square tiles, and instruct them to use the tiles to make a larger square. Have a class discussion in which students explain what they know about the new square. (Sample Answer: The new square is 2 tiles by 2 tiles. Its area is 4 square tiles.) Discuss the concepts of perfect squares and square roots. Squaring a number and finding the square root are inverse operations just as addition and subtraction “undo” each other. Indicate that a perfect square number gets its name because you can make a square with that number of given tiles; therefore, 4 is called a perfect square. You cannot make a square with 5 tiles, so 5 is not a perfect square. Another way of knowing if a number is a perfect square is by determining its square root. The square root of a perfect square is a whole number. =2; 22=4. Be sure students can distinguish between squares and square roots. Now, have two students use their combined blocks to make the biggest square possible. Have groups explain their solution and reasoning. The largest square possible measures 2 by 2; the next biggest square would be 3 by 3 or 9 square tiles. The students only have 8 tiles. 8 is not a perfect square; there is no whole number that can be multiplied by itself (squared) to get 8.Have students use other sums of square tiles to model perfect squares. Instruct students to find the first twenty perfect squares; 12=1, 22=4, 32=9, 42=16, and so on. Draw a number line on the board and number it from -20 to 20 (or more) on which students will determine the placement of square roots. Cut apart the problems on the Square Roots BLM or put similar problems on index cards. Examples of problems: What is the approximate value of? What is the value of? Make sure to have several types of problems. Pass out all cards to the students. Have a student read his/her card aloud, and place a mark on the number line where he/she thinks the answer belongs. Have a class discussion about the placement of the number on the number line each time. Ask questions regarding the placement of the answers. Example: Is your answer for the closer to 2 or 3? Why? Continue until all problems have been read aloud and the answers placed on the number line. Have students respond to the following prompt in their math learninglogs (view literacy strategy descriptions): Is closer to 4 or 5? Justify your reasoning with words, numbers, and a number line. 3. Review the meaning of “squaring a number.” Have student volunteer come up and model 5².
5 units
5 units
5 units
||
Answer: 5 x 5 = 25 or 5² = 25 square units 25 is the square of 5. Sometimes you will need to work backwards and are given a square (25) and you need to find the number that was squared (5). Give students this example: Think of a square that contains 36 blocks. How long is each side of the square? (6 blocks) 36 is the square of 6. Six is called the square root of 36. Think of a square that contains 100 blocks. What is the length of the square? (10 blocks) Ten is the square root of 100. (Model if necessary) 4. Write these sentences on the board. 100 is the square of 10. 10 is the square root of 100. 100 = 10² 10 = Have the students discuss the above statements. Possible discussions: 10² = 100, so 100 is the square of 10. Ten is the square root of 100, or the square root of 100 is 10. You can use the sign ( ) to show that you are taking the square root of a number. ASK: What is the square root of 64? Howcan you prove your answer is correct? (8) What is ? (3) What do you think it means to be a “perfect square”? (A perfect square is a square whose sides are whole numbers, such as a square with an area of 4 square units has sides of 2 units, but a square with an area of ‘3’square units has sides of about 1.7 units, not a whole number so ‘3’ is not a perfect square) 5. Have students work in pairs and come up with all of the perfect squares that are less than or equal to 100. Answer: (1, 4, 9, 16, 25, 36, 49, 64, 81, 100)Relate these numbers to squares and the square root to the length of the sides of these squares. 6. Say: Sometimes you may be asked to find the square root of a number that is not a “perfectsquare”. Does anyone know what to for these types of numbers? Put the following on the board: Ask the students to come up with possible ways to estimate the answer to the square root of 7. (Possible thoughts—The square root of 4 is 2 and the square root of 9 is 3 so the answer must be somewhere between 2 and 3. Since 7 is only 2 units away from 9 and 7 is 3 units away from 4, the square root of 7 is closer to 3 than 2. ) 7. Draw a number line on the board and number it from -20 to 20 (or more) on which students will determine the placement of square roots. 8. On index cards, have problems written for the students to use. Examples of problems: What is the approximate value of, What is the value of? Make sure to have several types of problems. 9. Give each student 4 square tiles, and instruct them to use the tiles to make a larger square. Have a class discussion in which students explain what they know about the new square. (Sample Answer: The new square is 2 tiles by 2 tiles. Its area is 4 square tiles.) Discuss the concepts of perfect squares and square roots. Squaring a number and finding the square root are inverse operations just as addition and subtraction “undo” each other. Indicate that a perfect square number gets its name because you can make a square with that number of given tiles; therefore, 4 is called a perfect square. You cannot make a square with 5 tiles, so 5 is not a perfect square. Another way of knowing if a number is a perfect square is by determining its square root. The square root of a perfect square is a whole number. =2; 22=4. Be sure students can distinguish between squares and square roots.
Now, have two students use their combined blocks to make the biggest square possible. Have groups explain their solution and reasoning. The largest square possible measures 2 by 2; the next biggest square would be 3 by 3 or 9 square tiles. The students only have 8 tiles. 8 is not a perfect square; there is no whole number that can be multiplied by itself (squared) to get 8.
Have students use other sums of square tiles to model perfect squares. Instruct students to find the first twenty perfect squares; 12=1, 22=4, 32=9, 42=16, and so on. Draw a number line on the board and number it from -20 to 20 (or more) on which students will determine the placement of square roots. Cut apart the problems on the Square Roots BLM or put similar problems on index cards. Examples of problems: What is the approximate value of? What is the value of? Make sure to have several types of problems. Pass out all cards to the students. Have a student read his/her card aloud, and place a mark on the number line where he/she thinks the answer belongs. Have a class discussion about the placement of the number on the number line each time. Ask questions regarding the placement of the answers. Example: Is your answer for the closer to 2 or 3? Why? Continue until all problems have been read aloud and the answers placed on the number line. Have students respond to the following prompt in their math learninglogs (view literacy strategy descriptions): Is closer to 4 or 5? Justify your reasoning with words, numbers, and a number line. 10. Pass out all cards to the students, have a student read his/her card aloud, and place a mark on the number line where he/she thinks the answer belongs. 11. Have a class discussion about the placement of the number on the number line each time. Ask questions regarding the placement of the answers. Example: Is your answer for the closer to 2 or 3? Why?. Continue until all problems have been read aloud and the answers placed on the number line. 12. Student Activity 7.3 What’s My Value? Homework Monday 13. Transparency 7.2 Answers: 1. 16 feet 2. a little over 5 feet for each side of the patio Tuesday ILEAP page 23 Check homework and go over 14. Student Activity 7.1 on ELMO - have students put answers on board Remind them of closeness to a number and what to do with negatives Have students work in groups to place numbers on the number line 14. Student Activity 7.2 Guided Practice or could be used for a grade. Homework Tuesday Answers: 1.- 9, b. 7, c. 6, d. 1, e. 12, f. 10 2. No the is closer to the square root of 81, therefore the I a little over 9. 3. The is a little more than 6, because the is 6 and is a little more than . 4. The is found between the whole numbers 4 and 5, closer to 5. 5. d. 121 and e. 1 6. The length of each side is 60 centimeters. 7. Each side is 12 inches. 8. x = 64 9. Any numbers from 82 to 99 will work. 16 Additional Resources:Text: Estimating Square Roots 11-2 pg. 475-477 RM: 614-6 18 17 Student Activity 7.4/iLEAP Connection answer: 1) d between 5 and 6; 2) d 12 feet; 3) c; 4) b 18 losure on Transparency 7.1 Modifications: Teacher Reflections: Grasp It! The student can determine the square root of perfect squares and mentally approximate other square roots by identifying the two whole numbers between which they fall.
GLE’S Addressed:
#12 Evaluate algebraic expressions containing exponents (especially 2 and 3) and square roots, using substitution (A-1-M)
#13 Determine the square root of perfect squares and mentally approximate other square roots by identifying the two whole numbers between which they fall (A-1-M)
#39 Analyze and describe simple exponential number patterns (e.g., 3, 9, 27 or 31, 32, 33) (P-1-M)
Objective(s)
1. The student will evaluate expressions containing exponents (especially 2 and 3) and square roots, using substitution.
2. The student will determine the square root of perfect squares and mentally approximate other square roots by identifying the two whole numbers between which they fall.
3. The student will analyze and describe simple exponential number patterns.
Materials:
Daily problem Transparency 7.1
3 boxes of graduated sizes
Student Activity 7.1
Transparency 7.2
Student Activity 7.2
Student Activity 7.3/ Homework “What’s My Value?”
Student Activity 7.4/iLEAP Connection
Index cards for number line in action #7
Text: Estimating Square Roots 11-2 pg. 475-477 RM: 614-618
iLEAP booklet pages 22, 23
Daily Problem Lesson 7
Make the correct substitutions on the left from the given values on the right.
1.
7 a. x
82. x² = 9 b. x = 49
3. x³ = 8 c. x = 3
4.
x d. x
2Answer= 1 – b, 2 – c, 3 –d, 4 - a
Have the students come up with their own definition of “square root.” Use the square feet models that were made in lesson 6 to help them see the ‘square root’ relationship to area.
Lesson Procedure
1. Discuss Daily Problem.
2. Give each student 4 square tiles, and instruct them to use the tiles to make a larger square. Have a class discussion in which students explain what they know about the new square. (Sample Answer: The new square is 2 tiles by 2 tiles. Its area is 4 square tiles.) Discuss the concepts of perfect squares and square roots. Squaring a number and finding the square root are inverse operations just as addition and subtraction “undo” each other. Indicate that a perfect square number gets its name because you can make a square with that number of given tiles; therefore, 4 is called a perfect square. You cannot make a square with 5 tiles, so 5 is not a perfect square. Another way of knowing if a number is a perfect square is by determining its square root. The square root of a perfect square is a whole number. =2; 22=4. Be sure students can distinguish between squares and square roots. Now, have two students use their combined blocks to make the biggest square possible. Have groups explain their solution and reasoning. The largest square possible measures 2 by 2; the next biggest square would be 3 by 3 or 9 square tiles. The students only have 8 tiles. 8 is not a perfect square; there is no whole number that can be multiplied by itself (squared) to get 8.Have students use other sums of square tiles to model perfect squares. Instruct students to find the first twenty perfect squares; 12=1, 22=4, 32=9, 42=16, and so on. Draw a number line on the board and number it from -20 to 20 (or more) on which students will determine the placement of square roots. Cut apart the problems on the Square Roots BLM or put similar problems on index cards. Examples of problems: What is the approximate value of ? What is the value of ? Make sure to have several types of problems.
Pass out all cards to the students. Have a student read his/her card aloud, and place a mark on the number line where he/she thinks the answer belongs.
Have a class discussion about the placement of the number on the number line each time. Ask questions regarding the placement of the answers. Example: Is your answer for the closer to 2 or 3? Why? Continue until all problems have been read aloud and the answers placed on the number line.
Have students respond to the following prompt in their math learning logs (view literacy strategy descriptions):
Is closer to 4 or 5? Justify your reasoning with words, numbers, and a number line.
3. Review the meaning of “squaring a number.” Have student volunteer come up and model 5².
5 units
||
Answer:
5 x 5 = 25 or 5² = 25 square units
25 is the square of 5. Sometimes you will need to work backwards and are given a
square (25) and you need to find the number that was squared (5).
Give students this example: Think of a square that contains 36 blocks. How long is each side of the square? (6 blocks) 36 is the square of 6. Six is called the square root of 36. Think of a square that contains 100 blocks. What is the length of the square? (10
blocks) Ten is the square root of 100. (Model if necessary)
4. Write these sentences on the board.
100 is the square of 10.
10 is the square root of 100.
100 = 10² 10 =
Have the students discuss the above statements.
Possible discussions: 10² = 100, so 100 is the square of 10. Ten is the square root of 100, or the
square root of 100 is 10. You can use the sign ( ) to show that you are
taking the square root of a number.
ASK: What is the square root of 64? How can you prove your answer is correct? (8)
What is ? (3)
What do you think it means to be a “perfect square”? (A perfect square is a square whose sides are whole numbers, such as a square with an area of 4 square units has sides of 2 units, but a square with an area of ‘3’square units has sides of about 1.7 units, not a whole number so ‘3’ is not a perfect square)
5. Have students work in pairs and come up with all of the perfect squares that are less than or equal to 100. Answer: (1, 4, 9, 16, 25, 36, 49, 64, 81, 100)Relate these numbers to squares and the square root to the length of the sides of these squares.
6. Say: Sometimes you may be asked to find the square root of a number that is not a “perfect square”. Does anyone know what to for these types of numbers?
Put the following on the board:
Ask the students to come up with possible ways to estimate the answer to the square root of 7.
(Possible thoughts—The square root of 4 is 2 and the square root of 9 is 3 so the answer must be somewhere between 2 and 3. Since 7 is only 2 units away from 9 and 7 is 3 units away from 4, the square root of 7 is closer to 3 than 2. )
7. Draw a number line on the board and number it from -20 to 20 (or more) on which students will determine the placement of square roots.
8. On index cards, have problems written for the students to use. Examples of problems: What is the approximate value of , What is the value of ? Make sure to have several types of problems.
9. Give each student 4 square tiles, and instruct them to use the tiles to make a larger square. Have a class discussion in which students explain what they know about the new square. (Sample Answer: The new square is 2 tiles by 2 tiles. Its area is 4 square tiles.) Discuss the concepts of perfect squares and square roots. Squaring a number and finding the square root are inverse operations just as addition and subtraction “undo” each other. Indicate that a perfect square number gets its name because you can make a square with that number of given tiles; therefore, 4 is called a perfect square. You cannot make a square with 5 tiles, so 5 is not a perfect square. Another way of knowing if a number is a perfect square is by determining its square root. The square root of a perfect square is a whole number. =2; 22=4. Be sure students can distinguish between squares and square roots.
Now, have two students use their combined blocks to make the biggest square possible. Have groups explain their solution and reasoning. The largest square possible measures 2 by 2; the next biggest square would be 3 by 3 or 9 square tiles. The students only have 8 tiles. 8 is not a perfect square; there is no whole number that can be multiplied by itself (squared) to get 8.
Have students use other sums of square tiles to model perfect squares. Instruct students to find the first twenty perfect squares; 12=1, 22=4, 32=9, 42=16, and so on.
Draw a number line on the board and number it from -20 to 20 (or more) on which students will determine the placement of square roots. Cut apart the problems on the Square Roots BLM or put similar problems on index cards. Examples of problems: What is the approximate value of ? What is the value of ? Make sure to have several types of problems.
Pass out all cards to the students. Have a student read his/her card aloud, and place a mark on the number line where he/she thinks the answer belongs.
Have a class discussion about the placement of the number on the number line each time. Ask questions regarding the placement of the answers. Example: Is your answer for the closer to 2 or 3? Why? Continue until all problems have been read aloud and the answers placed on the number line.
Have students respond to the following prompt in their math learning logs (view literacy strategy descriptions):
Is closer to 4 or 5? Justify your reasoning with words, numbers, and a number line.
10. Pass out all cards to the students, have a student read his/her card aloud, and place a mark on the number line where he/she thinks the answer belongs.
11. Have a class discussion about the placement of the number on the number line each time. Ask questions regarding the placement of the answers. Example: Is your answer for the closer to 2 or 3? Why?. Continue until all problems have been read aloud and the answers placed on the number line.
12. Student Activity 7.3 What’s My Value? Homework Monday
13. Transparency 7.2 Answers: 1. 16 feet 2. a little over 5 feet for each side of the patio
Tuesday
ILEAP page 23
Check homework and go over
14. Student Activity 7.1 on ELMO - have students put answers on board
Remind them of closeness to a number and what to do with negatives
Have students work in groups to place numbers on the number line
14. Student Activity 7.2 Guided Practice or could be used for a grade. Homework Tuesday
Answers: 1.- 9, b. 7, c. 6, d. 1, e. 12, f. 10
2. No the is closer to the square root of 81, therefore the I a little over 9.
3. The is a little more than 6, because the is 6 and is a little more than .
4. The is found between the whole numbers 4 and 5, closer to 5.
5. d. 121 and e. 1
6. The length of each side is 60 centimeters.
7. Each side is 12 inches.
8. x = 64
9. Any numbers from 82 to 99 will work.
16 Additional Resources: Text: Estimating Square Roots 11-2 pg. 475-477 RM: 614-6 18
17 Student Activity 7.4/iLEAP Connection
answer: 1) d between 5 and 6; 2) d 12 feet; 3) c; 4) b
18 losure on Transparency 7.1
Modifications:
Teacher Reflections:
Grasp It!
The student can determine the square root of perfect squares and mentally approximate other square roots by identifying the two whole numbers between which they fall.